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However, when the training data is corrupted, it has been well-known that over-parameterized networks tend to overfit and do not generalize. In this work, we propose a principled approach for robust training of over-parameterized deep networks in classification tasks where a proportion of training labels are corrupted. The main idea is yet very simple: label noise is sparse and incoherent with the network learned from clean data, so we model the noise and learn to separate it from the data. Specifically, we model the label noise via another sparse over-parameterization term, and exploit implicit algorithmic regularizations to recover and separate the underlying corruptions. Remarkably, when trained using such a simple method in practice, we demonstrate state-of-the-art test accuracy against label noise on a variety of real datasets. Furthermore, our experimental results are corroborated by theory on simplified linear models, showing that exact separation between sparse noise and low-rank data can be achieved under incoherent conditions. The work opens many interesting directions for improving over-parameterized models by using sparse over-parameterization and implicit regularization.","url_abs":"https://arxiv.org/abs/2202.14026v2","url_pdf":"https://arxiv.org/pdf/2202.14026v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"robust-training-under-label-noise-by-over","repo_url":"https://github.com/shengliu66/sop","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"learning-with-noisy-labels","task_name":"Learning with noisy labels"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/learning-with-noisy-labels-on-cifar-100n","task":"Learning with noisy labels","dataset":"CIFAR-100N","model":"SOP+","rank_in_archive_order":5,"of":24,"metrics":{"Accuracy (mean)":"67.81"},"uses_additional_data":false},{"leaderboard":"/sota/learning-with-noisy-labels-on-cifar-10n","task":"Learning with noisy labels","dataset":"CIFAR-10N-Aggregate","model":"SOP+","rank_in_archive_order":4,"of":26,"metrics":{"Accuracy (mean)":"95.61"},"uses_additional_data":false},{"leaderboard":"/sota/learning-with-noisy-labels-on-cifar-10n-1","task":"Learning with noisy labels","dataset":"CIFAR-10N-Random1","model":"SOP+","rank_in_archive_order":4,"of":24,"metrics":{"Accuracy (mean)":"95.28"},"uses_additional_data":false},{"leaderboard":"/sota/learning-with-noisy-labels-on-cifar-10n-2","task":"Learning with noisy labels","dataset":"CIFAR-10N-Random2","model":"SOP","rank_in_archive_order":2,"of":23,"metrics":{"Accuracy (mean)":"95.31"},"uses_additional_data":false},{"leaderboard":"/sota/learning-with-noisy-labels-on-cifar-10n-3","task":"Learning with noisy labels","dataset":"CIFAR-10N-Random3","model":"SOP+","rank_in_archive_order":2,"of":23,"metrics":{"Accuracy (mean)":"95.39"},"uses_additional_data":false},{"leaderboard":"/sota/learning-with-noisy-labels-on-cifar-10n-worst","task":"Learning with noisy labels","dataset":"CIFAR-10N-Worst","model":"SOP+","rank_in_archive_order":5,"of":25,"metrics":{"Accuracy (mean)":"93.24"},"uses_additional_data":false}],"syntology":{"syntology_url":"https://syntology.ai/paper/2202.14026","atlas_url":"https://app.syntology.ai/?focus=2202.14026","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2202.14026"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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